| Nuclear planetology [1] is a new research field, tightly constrained by a coupled
187Re-232Th-238U systematics [2-6], which by means of nuclear astrophysics aims also at
understanding the thermal evolution of Earth-like planets after Mercury-like contraction and
Fermi-pressure controlled gravitational collapse events towards the end of their cooling
period. In nuclear planetology, Earth-like planets are regarded as old (redshift z >15),
down-cooled and differentiated black dwarfs (Fe-C BLD’s), so-called interlopers from the
Galactic bulge [7], which are subjected to endoergic 56Fe(γ,α)52Cr (etc.) reactions
(photodisintegration), (γ,n) or (γ,p) and fusion reactions like 12C(α,γ)16O. It is remarkable
that, beside of its surface temperature Teff of its outer core surface, the Earth shows also
striking similarity in volume V (radius rEarth ≈6.370 km) with an old white dwarf star
(WD; rWD ≈6.300 km) like WD0346+246. This major boundary condition for nuclear
planetology can be described in terms of V Earth = V WD = V const=4•π•r3/3
(rWD ≈ rEarth). However, in addition to the fact that Earth is habitable, the most
obvious difference between a WD and the Earth is their density ρ (ρ=m/V; m mass, V
volume): while a WD may contain 1MO(MO= solar mass) per V const, the mass of the
Earth is only a tiny fraction of this, ≈3•10−6 MO per V const. Therefore, it is
crucial to understand ∂ρ, or why mEarth«mWD for V const. Here I argue that the
application of principles constrained by the theory of relativity [8] may offer a
possible answer to this question: it is generally accepted that mass is directly related to
energy, E=m•c2 (E energy; m mass; c velocity of light) or m=E/c2. From m∼E
we derive that any mass change can be described in terms of energy change [8].
Instead of ρ=m/V we may thus write ρ=E/c2•V, and because of the special scenario
V Earth = V WD = V const discussed here, the denominator of this equation becomes a
constant term C=c2•Vconst =9.73•1037m5s−2. From this it follows, that ρ=E/C, or ρ•C=E.
Therefore, we arrive at ρ ∼E for the WD/FeC-BLD case or, considering the evolution of the
system over time t: ∂ρ/∂t∼∂E∕∂t.Hence, concerning time integrated planetary
evolution it may be concluded that any density change ∂ρ of an old stellar remnant
towards a ≈3•10−6 MO habitable Earth-like planet is a measure for the system’s
energy change ∂E. In the light of nuclear planetology this result has to be considered
to understand the formation and evolution of crusts and mantles on planets and
moons.
[1] Roller (2015), Abstract T34B-0407, AGU Spring Meeting 2015. [2] Roller (2015),
Goldschmidt Conf. Abstr. 25, 2672. [3] Roller (2016), Goldschmidt Conf. Abstr. 26, 2642. [4]
Roller (2016), JPS Conf. Proc., Nuclei in the Cosmos (NIC XIV), Niigata, Japan, subm.
(NICXIV-001); NICXIV Abstr. #1570244284. [5] Roller (2016), JPS Conf. Proc., Nuclei
in the Cosmos (NIC XIV), Niigata, Japan, subm. (NICXIV-002); NICXIV Abstr.
#1570244285). [6] Roller (2016), JPS Conf. Proc., Nuclei in the Cosmos (NIC XIV),
Niigata, Japan, subm. (NICXIV-003); NICXIV Abstr. #1570244281. [7] Howes et al.
(2015), Nature 527, 484-487. [8] Einstein (1905), Annalen d. Physik, 18, 639-641. |